Variations of the Energy of Free Particles in the pp-Wave Spacetimes

TL;DR

This paper studies how free particles' kinetic energy varies when passing through exact plane gravitational waves (pp-waves), revealing quasi-periodic energy variations linked to wave parameters, and explores implications for gravitational energy localization.

Contribution

It provides a numerical analysis of energy variations of free particles in pp-waves, highlighting quasi-periodic behavior and estimating gravitational energy changes during wave interactions.

Findings

Kinetic energy of particles shows quasi-periodic variation with wave width.

Energy variation correlates with the gravitational field's energy change.

Impulsive wave behavior emerges in the Gaussian wave limit.

Abstract

We consider the action of exact plane gravitational waves, or pp-waves, on free particles. The analysis is carried out by investigating the variations of the geodesic trajectories of the particles, before and after the passage of the wave. The initial velocities of the particles are non-vanishing. We evaluate numerically the Kinetic energy per unit mass of the free particles, and obtain interesting, quasi-periodic behaviour of the variations of the Kinetic energy with respect to the width $\lambda$ of the gaussian that represents the wave. The variation of the energy of the free particle is expected to be exactly minus the variation of the energy of the gravitational field, and therefore provides an estimation of the local variation of the gravitational energy. The investigation is carried out in the context of short bursts of gravitational waves, and of waves described by normalised gaussians, that yield impulsive waves in a certain limit.